Most begonias are tender perennials. If you live in central to southern FL or CA then you can grow them outside year round. Being in IL you can grow them outside in warmer months but must bring them inside for winter. Give them ample light (next to a window or fluorescent light) and water on a regular basis and they should do fine. Do be forewarned that Madame Queen can be finicky so a terrarium may be more fitting for it (too much water and it will rot, too dry and it will die). MQ can get very large so a big terrarium is what you need. I have not grown Black Truffles but I would suspect it to be quite easy without a terrarium. Give both a fast draining soil and never allow to dry out completely but then do NOT keep it sopping wet either.

Check out Brad Thompson's World of Begonias. It is a good starting point for newbies on growing begonias.

Brad Thompson

Your discovery is one of the fun things for me about rhizomatous begonias. They get mixed in as annuals at many garden centers in the spring. Names are not provided, so the research begins. Usually you need to go to a begonia garden club sale, online or specialty nurseries that are few. I keep my rhizos in a southern window on pebbled trays on low black greenhouse benches. Early winter sun can be a bit strong, so a light curtain then. I used to put them out under trees in my Maryland garden for a summer break but insects and some brutal heat/downpours made me decide my air conditioning was the lesser evil. I have a Madame Queen who is indeed queenly: looks like a big, upright fancy lettuce plant. I take one or two out of the group and give them center stage in another room for about a week, then it's back to the high humidity they go or they'll get brown edges very quickly.